This talk will survey the calculations of matrix elements of quark
bilinear operators between nucleon states using lattice QCD . A number
of exciting physics, at the intersection of nuclear and particle
physics, is being probed using these calculations. The axial charge
g_A is a fundamental parameter encapsulating the weak interaction of
nucleons and serves to benchmark the efficacy of lattice QCD
calculations of nucleon structure. The scalar and tensor charges, g_S
and g_T, combined with precision neutron decay distribution probe
novel scalar and tensor interactions at the TeV scale. Vector form
factors are probed in electron scattering, while axial vector form
factors are used in the calculation of the cross-section of neutrinos
on nuclear targets. These energy dependent cross-sections are needed
to determine the neutrino flux, an important systematic in neutrino
oscillation experiments. Flavor diagonal charges are needed to quantify
the interaction of dark matter with nuclear targets and for the nucleon
sigma term. Lastly I will provide results for the matrix elements of two
novel CP violating operators, the quark EDM and the quark Chromo EDM ,
that contribute to the electric dipole moment of the neutron (nEDM).